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NBER WORKING PAPER SERIES
THE DIVERGENCE OF HUMANCAPITAL LEVELS ACROSS CITIES
Christopher R. BerryEdward L. Glaeser
Working Paper 11617http://www.nber.org/papers/w11617
NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue
Cambridge, MA 02138September 2005
Glaeser thanks the Taubman Center for State and Local Government for financial support. Lawrence Katzand three anonymous referees provided very helpful comments. The views expressed herein are those of theauthor(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
©2005 by Christopher R. Berry and Edward L. Glaeser. All rights reserved. Short sections of text, not toexceed two paragraphs, may be quoted without explicit permission provided that full credit, including ©notice, is given to the source.
The Divergence of Human Capital Levels Across CitiesChristopher R. Berry and Edward L. GlaeserNBER Working Paper No. 11617September 2005JEL No. J0
ABSTRACT
Over the past 30 years, the share of adult populations with college degrees increased more in cities
with higher initial schooling levels than in initially less educated places. This tendency appears tobe driven by shifts in labor demand as there is an increasing wage premium for skilled peopleworking in skilled cities. In this paper, we present a model where the clustering of skilled people inmetropolitan areas is driven by the tendency of skilled entrepreneurs to innovate in ways that employ
other skilled people and by the elasticity of housing supply.
Christopher R. BerryHarris School of Public PolicyUniversity of Chicago1155 E. 60th Street, Suite 179Chicago, IL [email protected]
Edward L. GlaeserDepartment of Economics315A Littauer CenterHarvard UniversityCambridge, MA 02138and [email protected]
2
I. Introduction
U.S. metropolitan areas with more college graduates in 1990 became increasingly skilled
over the 1990s. Figure 1 shows a 52 percent correlation between the initial share of
adults with college degrees in 1990 and the growth in the share of adults with college
degrees between 1990 and 2000 across metropolitan areas. A one percent increase in
the share of adults with college degrees in the 1990s is associated with a .13 percent
increase in the share of the population with college degrees between 1990 and 2000. The
correlation between initial share of the population with college degrees and growth in that
share was 44 percent in the 1980s and 60 percent in the 1970s.
In Section II of this paper, we document this divergence of skill levels. There is a strong
correlation between changes in the share of the adult population with college degrees and
the initial share of the population that is well educated and this is robust to a wide number
of controls. This relationship is also robust to following Moretti (2004) and using
colleges per capita in 1940 as an instrument for initial skill levels. This tendency of
initially skilled places to become more skilled over time has, so far, caused only very
modest increases in segregation by skill across metropolitan areas. Traditional measures
of segregation such as isolation and dissimilarity indices show a small rise over the past
30 years. Still, segregation by skill across metropolitan area remains quite modest.
In Section III, we present a simple model of urban agglomeration that can potentially
explain the increased tendency of skilled people to move to initially skilled areas. The
core assumption of the model is that the number of entrepreneurs is a function of the
number of skilled (and unskilled) people working in an area. This model departs from
traditional regional models by assuming that new entrepreneurs are, at least for a time,
relatively immobile. If skilled people are more likely to innovate in ways that employ
other skilled people then this creates an agglomeration economy where skilled people
want to be around each other.
3
The model can explain the observed changes over time through two mechanisms. First, if
the tendency of skilled entrepreneurs to particularly hire skilled people has increased over
time, then this would explain why skilled people come to initially skilled cities. Second,
if housing supply has become more inelastic over time, then unskilled people will face
increasingly higher prices to live around skilled people and move to cheaper places.
In Section IV, we evaluate these explanations. Cross-industry evidence shows that there
has been more innovation in skilled sectors of the economy and new firms generally
employ the skilled (Abowd et al., 2001). We find an increasing correlation across
industries between managerial skills and worker skills. In 1970, the correlation across
industries between the share of managers with college degrees and the share of workers
with college degrees was 38 percent. In 2000, that same correlation coefficient reached
51 percent. A one percentage point increase in the share of managers with college
degrees in 1970 was associated with a .15 percentage point increase in the share of
workers with college degrees. In 2000, a one percentage point increase in the share of
managers with college degrees was associated with a .38 percentage point increase in
share of workers’ college degrees. The tendency of skilled managers to employ skilled
workers has clearly increased over time. We take all of this as evidence supporting the
view that skilled entrepreneurs increasingly provide employment opportunities primarily
for skilled workers.
The evidence for the housing supply inelasticity hypothesis is more mixed. While there
is significant evidence suggesting that housing supply is more inelastic now than in the
past, there is little evidence suggesting that this explains the increased tendency of skilled
people to move into skilled areas. The relationship between metropolitan area skill levels
and housing prices has remained relatively constant between 1980 and today.
Controlling for initial housing price levels does not reduce the correlation between initial
skills and later skill growth.
In Section V of this paper, we explore the predictions of the model for wage and income
patterns across metropolitan areas. As the model suggests, there is an increasingly tight
4
relationship between education and income at the metropolitan area level. In 1970, the
correlation between share of adults with college degrees and the log of income in the
metropolitan area was 21 percent. In 2000, that correlation rose to 63 percent. When we
hold individual education constant, the correlation between metropolitan area education
and individual wages has also risen and this rise has been much more pronounced for
high skilled workers. This finding supports the view that our core fact is the result of
increasing demand for high skilled workers in initially high skill cities.
Finally, we document that the divergence of skill levels seems related to the decline of
income convergence across metropolitan areas (Barro and Sala-i-Martin, 1992). In the
1970s, the correlation between initial wages and wage growth was –36 percent. In the
1990s, this correlation switched signs and became 15 percent. While the end of regional
convergence certainly does not imply a need for policy intervention, it does at least mean
that we cannot expect that differences in income across space will naturally disappear.
II. Evidence on Skill Divergence
In this section, we review the basic facts that motivate this paper. First, we present the
evidence on the relationship between changes in the share of skilled individuals at the
metropolitan area level and the initial share of individuals who are skilled. Second, we
examine whether the increase in skills can be explained by industrial shifts in skilled
cities. Third, we present evidence on the segregation of the skilled within the United
States.
The Correlation between Increase in Skills and Initial Skills
We begin with our most basic relationship: the connection between growth in the
percentage of adults with college degrees and the initial share of people in the area with
college degrees. We estimate:
(1) εβα ++•+=−+ ControlsOtherCollegeCollegeCollege ttt 1 ,
5
where tCollege refers to the share of the adult population at time t with sixteen years of
schooling or more. Our units of observation are all 318 metropolitan statistical areas and
primary metropolitan statistical areas (NECMA definitions in New England). Unless
otherwise noted, all data come from the 1970, 1980, 1990, and 2000 US censuses. We
rely on county level data from each census aggregated to a consistent set of 1999
metropolitan area boundaries.1
Table 1 shows our first set of regressions. Regression (1) of Table 1 quantifies the
relationship, shown in Figure 1, between the growth in the share of population with
college degrees and the initial share of the population with degrees in the 1990s with no
other controls. In this regression, the r-squared is 27 percent and the coefficient is .13.
As the share of college graduates in the metropolitan area increased by 1 percent in 1990,
on average the share of adults with college degrees increased by 1.13 percentage points in
2000.
This coefficient does not merely reflect a tendency of skilled people to come to certain
areas in recent years. Following Moretti (2004), we can use the number of colleges per
capita in the metropolitan area in 1940 as a measure of the area’s long term commitment
to human capital. There is a 23 percent correlation between the number of colleges in the
metropolitan area in 1940 and the growth in the share of adults with college degrees
between 1990 and 2000. When we use the number of colleges per capita in 1940 as an
instrument for the share of the adult population with college degrees in 1990, we
estimate:
(2) 1990)048(.)009(.19902000 217.006. CollegeCollegeCollege •+−=− .
The relationship between initial skills and growth in skill is, if anything, stronger, when
we use this historic measure of human capital as an instrument for schooling in 1990.
1 The data set is described further in the appendix of Glaeser and Saiz (2004).
6
In regression (2) of Table 1, we include standard controls for four region dummies, the
logarithm of the initial level of income, the logarithm of the initial population level, and
the initial share of the population working in manufacturing industries. Regional effects
are weak and only the west had a discernibly lower level of skill upgrading. There is also
no correlation between city size and growth of skills. Manufacturing cities had a slightly
higher increase in the share of their populations with college degrees. Initial income also
predicts an increase in the share of the growth in college graduates. While many of these
effects are significant, they only modestly reduce the coefficient on the initial share of the
population with college degrees from .13 to .11.
Regression (3) of Table 1 reproduces regression (1) for the 1980s. In this decade the
correlation between initial skills and subsequent skill growth is weaker, but it is still
significant. The correlation coefficient between growth and initial level is 44 percent.
The coefficient in this regression is .13 which is almost the same as in the 1990s. Figure
2 shows this relationship. Comparing Figures 1 and 2 shows that in the 1990s, the most
highly skilled cities (often based around universities) increased their skill levels
substantially, but in the 1980s, the skill growth in these university towns was
considerably more modest.
Regression (4) of Table 1 reproduces regression (2) for the 1980s. In this case, including
the other controls causes the coefficient on the initial years of schooling to increase. One
change between the 1980s and 1990s is that initial income does not predict an increase in
the share of the adult population with college degrees between 1980 and 1990. A second
change is that metropolitan areas with more people became more skilled in the 1980s.
Regressions (5) and (6) of Table 1 reproduce regressions (1) and (2) for the 1970s. In
this decade, the raw correlation between the initial share of the adult population with
college degrees and later growth in this measure is at its strongest. The coefficient in
regression (5) is .24 and the r-squared is 36 percent. Adding other controls again makes
little difference to this coefficient. In this decade, both initial population and initial
7
income predict an increase in the share of the population with college degrees, but during
this decade manufacturing cities were less likely to increase the share of their population
with sixteen years of schooling or more.
The functional form of equation (1) is somewhat problematic since the change in a share
cannot be distributed normally. Furthermore, this dependent variable corresponds weakly
to the standard structure of urban growth regressions. In Table 2, we instead estimate:
(3) εβα +•+=���
����
� +t
t
t CollegeLog 111
BAs with AdultsBAs with Adults
and
(4) εβα +•+=���
����
� +t
t
t CollegeLog 221
BAs w.o.AdultsBAs w.o.Adults
where tBAs wAdults refers to the number of college educated adults in the metropolitan
area as of time t and tBAs w.o.Adults refers to the number of adults with less than
sixteen years of schooling in the metropolitan area during the same year. We focus on
the difference between 1β , the impact of the initial college variable on growth in the
number of adults with sixteen years of schooling or more and 2β , the impact of the
initial college variable on growth in the number of adults with less than sixteen years of
schooling. We omit other controls to make comparisons between the coefficients more
straightforward.
Regression (1) of Table 2 shows the results for the 1990s. The coefficient on the lagged
share of the population with college degrees is positive and significant at the 10 percent
level. A .01 increase in the share of people with sixteen years of schooling is associated
with a .002 log point increase in the growth of people with sixteen years of schooling.
The coefficient becomes significant at the five percent level and increases by more than
8
10 percent if Las Vegas is omitted from the sample. As has been previously noted
(Glaeser et al. 1995), the correlation between education and growth is often sensitive to
the inclusion of that single metropolitan area.
In regression (2) of Table 2, we look at the correlation between the initial share of the
population with college degrees and the growth in the adult population without college
degrees. In the 1990s, there is essentially no correlation. We are able to reject the
equality of the coefficients in regressions (1) and (2) at the 10 percent level. In
regressions (3) and (4) of Table 2, we repeat regressions (1) and (2) of Table 2 for the
1980s. In the 1980s, the impact of initial years of schooling on later population growth is
essentially identical for both college graduates and non-college graduates. A .01 increase
in the share of the population with college degrees is associated with .003 log point
increase in population growth for either population subgroup.
In regressions (5) and (6) of Table 2, we repeat this exercise for the 1970s and find that in
that decade the impact of college education is completely reversed. Places that were
better educated in 1970 added significant numbers of non-college graduates, but added
almost no more college graduates. A .01 increase in the share of the population with
college degrees is associated with .006 log point increase in population growth for non-
college graduates but a .0006 log point increase in population growth for college
graduates. The test of the equality of the coefficients in regressions (5) and (6) soundly
rejects.
Table 2 shows the transformation of the impact of college graduates on population
growth. In the 1970s, skilled cities grew by attracting unskilled workers. In the 1990s,
skilled cities grew by attracting skilled workers. The relationships are generally less
striking when we look at the logarithm of population because this concave transformation
emphasizes the growth in percent college educated of cities with a small initial number of
college graduates, but nonetheless these regressions continue to emphasize a changing
pattern where skills are increasingly attracting skills.
9
Is the connection between initial skills and skill upgrading the result of skilled industries
increasingly moving to skilled cities? To test this hypothesis, we construct an index that
predicts the level of skills in a metropolitan area based on its industrial composition and
the skill levels of industries at the national level. Each metropolitan area’s industrial skill
index is:
(5)in U.S.AIndustry in WorkersTotalin U.S.A. BAs .Industry win Workers
MSAin Employment TotalMSAin Industry in Employment
� •Industries
The index sums across industries the multiple of the industry’s share of MSA
employment and the average share of the industry with college degrees in the U.S. as a
whole. The index represents the share of workers with BAs in the MSA that would be
found if each industry in the MSA had the same share of BA workers as in the industry
nationwide. In other words, the index is a prediction of local educational attainment
based solely on the MSA’s industrial composition. This index is calculated for one-digit
industries. The industry share of MSA employment is from the Regional Economic
Information System (REIS) of the Bureau of Economic Analysis, and we calculate
education levels in each industry using the public use micro-samples (PUMS) of the U.S.
Census (Ruggles et al. 2004).
Table 3 reports results from regressions of changes in this index on the initial share of
adults in the metropolitan area with sixteen years of schooling or more. In the upper
panel we report coefficients from these regressions for the 1970s, 1980s and 1990s. The
upper panel shows the effect of initial schooling on increases in the skill level of
industries at the metropolitan area level. The first column gives results for the 1970s. In
that decade, initial skills did predict a transition into more skilled industries, but this
effect is weak relative to the overall connection between initial skills and skills growth.
In the 1980s and the 1990s, there is no connection between initial skills and industrial
shifts into more skilled industries. While these results are coarse and use only one-digit
industries, they certainly suggest that the impact of skills on skill upgrading is occurring
10
within industries. There is at best a small impact of initial skills on shifts into more
skilled industries.
In the lower panel of Table 3 our dependent variable is the change over the decade in the
difference between the actual share of adults in the metropolitan area with BAs and the
industrial skill index. The lower panel shows the impact of initial schooling on increases
in the skill level at the metropolitan area level beyond the skill changes predicted by
changes in industrial composition. In all three decades, the relationship is significant and
positive, indicating that initial attainment increases skills primarily through channels
other than industrial composition.
A Rise in the Segregation of the Skilled?
The inevitable counterpart of the correlation between growth in percentage of college
educated and the initial share of the population with sixteen years of schooling is that
cities are becoming more different in their educational bases. While segregation by skill
across metropolitan remains extremely modest, we have gone from a situation where
skills were remarkably evenly distributed across space to a situation where metropolitan
areas increasingly differ from one another on the basis of their human capital levels.
Table 4 shows the time path for education heterogeneity across metropolitan areas. The
first column of the table shows the remarkable increase in the mean level of schooling
over this period. In 1970, in the average metropolitan area, 11.2 percent of population
had college degrees. Even more remarkable, metropolitan areas were relatively
homogeneous in their years of schooling. The standard deviation of the share of the adult
population with college degrees in 1970 was .042. One half of metropolitan areas had
between 8.7 percent college graduates and 13.1 percent college graduates. This is shown
in the third column which gives the gap in percent college educated between the
metropolitan area that is more educated than exactly 25 percent of all metropolitan areas
11
and the metropolitan area that is more educated than exactly 75 percent of all
metropolitan areas.
In 1980, the average share of metropolitan areas with college degrees increased to 16.4
percent and the standard deviation rose to .054. The percentage increase in the mean
during this period was much larger than the percentage increase in the standard deviation,
so the coefficient of variation actually fell. Still, this does not lessen the fact that cities
were increasingly differentiating themselves on the basis of years of schooling during this
decade. The gap between 25th percentile and 75th percentile in the share of adults with
college degrees increased to 6.3 percent.
In the 1990s, the mean share of the population with college degrees increased further to
18.7 percent, and the standard deviation of this number across metropolitan areas
increased to .063. In 1990, the mean share of metropolitan area population with college
degrees increase to 22.6 percent and the standard deviation increased to .073. The gap
between the 25th percent and the 75th percentile continued to widen to 9.6 percentage
points. The rising standard deviation reflects the increasing weight in the tails of the
distribution. By 2000, there were 62 metropolitan areas with less than seventeen percent
of their adults had college degrees and 32 where more than thirty-four percent of their
adults had college degrees. Since the distribution is truncated below at zero, the most
impressive growth has been at the upper tail of the distribution. In 1970, no metropolitan
area had more than 30.8 percent of its adult population with college degrees. In 2000,
there were 49 metropolitan areas where more than 30.8 percent of adult population had
sixteen years of schooling or more.
While there is clearly a correlation between change in the share of adults with college
degrees and the initial share of the population that is well educated, and it is clear that the
variance of these shares is rising over time, the changes in the segregation of the skilled
across metropolitan areas remain modest. Also in Table 4, we use standard measures
from the segregation literature to assess the degree to which the skilled are segregated
across metropolitan areas. Our first measure is the dissimilarity index:
12
(6) � −=MSAs
ityDissimilarBAs w.o.Adults Total
BAs w.o.AdultsBAs w.Adults Total
BAs w.Adults21 MSAMSA
where MSABAs w.Adults refers to the number of adults in the metropolitan area with
college degrees, MSABAs w.o.Adults refers to the number of adults in the metropolitan
area without sixteen years of schooling. This measure can be interpreted as the share of
people with sixteen years of schooling who would have to move for there to be a
completely even distribution of people with sixteen years of schooling across all
metropolitan areas.
Table 4 shows the time path of this index. Dissimilarity does rise over this period from
.11 to .128. These numbers are quite low relative to the segregation of other groups such
as African-Americans and they reflect the fact that skills are still distributed relatively
evenly over space. So while skilled people are becoming more segregated, this trend is
mild and the skilled still remain relatively integrated over space.
The second primary measure of segregation is the isolation index or:
(7) � −=MSAs
IsolationAdults Total
BAs w.Adults TotalBAs w.Adults Total
BAs w.AdultsAdults
BAs w.Adults MSA
MSA
MSA
where MSAAdults refers to the number of adults in the MSA and Adults Total refers to the
total number of adults across all metropolitan areas. The first term in the expression
averages across adults with sixteen years of schooling the average share of adults with
sixteen years of schooling in their metropolitan area. The second term subtracts off the
average share of adults with sixteen years of schooling in the sample as a whole. This
index captures the extent to which people with college degrees are surrounded only by
like people.
13
If we didn’t correct for the overall increase in the share of the population with college
degrees then the isolation index would rise from 12.8 percent to 28.2 percent over the
time period. At the start of the time period, on average someone with a college degree
lived in a metropolitan area where about one-eighth of the population had a similar
credential. Thirty years later, a typical person with a college degree lives in a
metropolitan area where more than one-in-four have the same amount of schooling.
But most of this gain reflects the rise in education generally and when we correct by
subtracting the sample wide share of the population with sixteen years of schooling, this
isolation index increases only from .008 to .016. This increase is real but modest and the
average college graduate lives in a metropolitan area that is only slightly better educated
than the average person without a college degree.
III. Sorting by Skills: Theory
In this section, we present a simple model of urban agglomeration which provides an
explanation for the tendency of skilled people to live among other skilled people. The
core assumption in the model is that the number of employers depends on the number of
people, and particularly, the number of skilled people in the area.2 We think of this as
reflecting a process where entrepreneurs come out of a city’s labor force and then tend to
stay generally in that area. Duranton and Puga (2001) present a more thorough
discussion of location decisions of innovators in urban areas.
While we will generally be treating firms as fixed, we assume that workers are mobile
and their utility in the city must be equal to their reservation utility which equals U for
skilled workers and U for unskilled workers. Utility for high skill workers in city “i”
equals: ( )( )Hi
Li
Hi
HHi ANNCWU ,+− ; utility for low skill workers equals
( )( )Li
Li
Hi
LLi ANNCWU ,+− . The variables L
iW and HiW refer to the endogenously
determined wages received in city i by low and high skill workers respectively. The
2 The link between population size and innovations is emphasized by Kremer (1993).
14
variables LiA and H
iA refer to the exogenous amenity levels in the city which can
disproportionately attract high and low skill individuals.
The terms ( )Li
Hi
H NNC + and ( )Li
Hi
L NNC + refer to the cost of living in city i
(primarily housing costs) which is a function of the sum of the total number of high skill
workers ( HiN ) and the total number of low skill workers ( L
iN ), and we denote this N.
We allow an increase in population to have different impacts on the cost of living for
both high and low skilled workers. The equations ( )( ) UANNCWU Hi
Li
Hi
HHi =+− , and
( )( ) UANNCWU Li
Li
Hi
LLi =+− ,, then determine the labor supply into this city. We can
use these two equalities to define implicit functions ( )( )Li
Hi
HHi
Hi NNCAW +, and
( )( )Li
Hi
LLi
Li NNCAW +, which reflect the wages that firms need to pay workers to induce
them to stay in a town of size N.
There are two types of firms each of which employs only one type of worker. Each firm
sells its product at a price of 1 and has access to a production technology: )( jj
i Qfθ
where j equals H or L, jQ refers to the number of workers hired by the firm, and f(.) is
monotonically increasing and concave. Each firm is assumed to be started by an
entrepreneur who receives the excess rents from the firm. The limiting factor to
entrepreneurship is assumed to be new ideas and these ideas occur stochastically in the
population. The number of entrepreneurs whose firms employ high type workers is
assumed to equal Hii Nhh 1φ+ . The term ih is an exogenous constant and the term
HiNh1φ assumes that the amount of entrepreneurship of this type is proportional to the
number of high skilled people living in this community. We are assuming that high skill
workers produce a new idea with probability 1h , and with probability φ this new idea
involves the employment of high skill workers. We also implicitly assume that there is
some natural comparative advantage to this location that ensures that these firms remain
in the area, or that new ideas are location-specific so that they cannot be taken elsewhere.
15
The number of entrepreneurs who open low skill firms equals Hi
Lii NhNll 11 )1( φ−++ .
The term il is again an exogenous constant. The term LiNl1 describes the number of low
skill firms started by low skill entrepreneurs. We assume that unskilled workers cannot
innovate in a way that employs more skilled workers. Finally, the term HiNh1)1( φ−
refers to the number of high skill entrepreneurs who start firms that employ less skilled
workers. The parameter φ is important in the model and captures the extent to which
high skill people come up with ideas that lead only to the employment of high skill
workers.
The assumption that the number of firms is proportional to the number of workers of each
type is the core of the model. This assumption embeds two different ideas. First, we are
assuming that innovations just occur randomly to workers. We are assuming that these
events are sufficiently rare in the life of most workers that they can be treated as being
measure zero in the location decision, but when they occur they create the possibility for
a new product that can produce sizable rents. Second, we are assuming that when a
worker has a new idea, that worker stays in his home area. This fixed nature of
employment can be justified if entrepreneurs want to stay in their cities for consumption
reasons or if the innovation makes use of unique aspects of their own urban environment.
This connection between population size and entrepreneurship is the key agglomeration
effect in this model. Workers are both providers of labor supply and potential innovators
who create labor demand. We have also assumed that unskilled workers only innovate in
firms that employ other unskilled workers, but that when skilled workers innovate with
probability φ they employ their own human capital type and with probability φ−1 they
employ workers of another human capital type. We think it is reasonable to assume that
people without education will have difficulty figuring out a new production process that
uses entirely people with more education, but it is possible that skilled people (like Henry
Ford) will occasionally develop firms that use less skilled workers.
16
With these assumptions the core equations of the model equate the marginal product of
labor for both high skilled firms and low skilled firms with the wage that is demanded by
workers to stay in that town, or ( )( )Li
Hi
HHi
HiH
ii
HiH
i NNCAWNhh
Nf +=��
�
����
�
+′ ,
1φθ and
( )( )Li
Hi
LLi
LiL
iHii
LiL
i NNCAWNlNhl
Nf +=��
�
����
�
+−+′ ,
)1( 11φθ . These equations do not
include any classic human capital externalities (as in Lucas, 1988), and the only benefit
for less skilled workers from living around the more skilled is actually a pecuniary
externality. If 0=ih , the model suggests that each firm has decreasing returns to skilled
workers, but that the city as a whole has constant returns to skilled workers.
Comparative statics then follow:
Proposition 1: The number of skilled people in the city will decline and the number of
unskilled people in the city will rise if Liθ , il or L
iA increase.
If ( )NC L '1 φ−
is sufficiently high, then an increase in Hiθ , il or H
iA will cause both
the number of skilled people and the number of unskilled people in the city to rise.
If ( )NC L '1 φ−
is sufficiently low, then an increase in Hiθ , il or H
iA will cause the
number of skilled people in the city to rise and the number of unskilled people in the city
to fall.
Proposition 1 provides the core results of this model. Parameters that increase the
attractiveness of the city for the less skilled, such as Liθ , il or L
iA , will cause the cost of
living to rise and skilled people leave the city. An increase in Liθ (the productivity of
less skilled firms) or il (the number of firms specializing in less skilled workers) will
create an increase in labor demand for the less skilled in that location. An increase in LiA reflects an amenity that particularly attracts the poor, such as more generous welfare
payments, will also repel the rich as it seems to have done in cases like East St. Louis.
17
The more interesting results concern the comparative statics on Hiθ , ih and H
iA . Because
an increase in the skilled leads to more firms that hire both the skilled and the unskilled it
is quite possible that a parameter that makes a place more attractive to the skilled will end
up attracting more unskilled as well. The impact of the skilled on the location of the
unskilled depends on the magnitude of ( )NC L '1 φ−
. The numerator of this expression
captures the extent to which the skilled are likely to produce innovations that employ the
unskilled. The denominator captures the extent to which an increase in the number of the
skilled living in the area drives up the cost of living for the unskilled.
When ( )NC L '1 φ−
is high, either because the skilled innovate in a way that employs the
unskilled or because ( )NC L ' is low, then we would expect the skilled and unskilled to
live together. Any location specific characteristic that attracts the skilled, such as a
consumption amenity ( HiA ), or the productivity of more skilled workers ( H
iθ ) or an
increase in the number of firms that hire the more skilled, will also attract more unskilled
people as well who will choose to locate near the skilled.
However if ( )NC L '1 φ−
is low, either because the skilled innovate in a way that only
employs the skilled or because ( )NC L ' is high, then the forces that attract the skilled will
tend to push the unskilled away. In this case, the impact of the skilled on the cost of
living overwhelms the impact of the skilled on the employment prospects for the less
skilled. Furthermore, in this scenario we should expect to see more clustering of skilled
and unskilled people in different metropolitan areas.
This proposition suggests two reasons why we should see an increasing tendency for
more skilled workers to go to cities that have advantages for the skilled. First,
innovations of the skilled may now tend to employ primarily skilled persons while in the
18
past, innovative firms founded by skilled people often employed large numbers of
unskilled people. In a sense this is a comparison between Henry Ford and Bill Gates.
Both individuals were themselves skilled, but Ford’s production involved vast numbers
of unskilled workers. Gates’ company primarily employs the more skilled.
A second reason why we should expect to see a change in the locational patterns of the
skilled and unskilled is increasing housing supply inelasticity. When housing supply is
sufficiently elastic so that ( )NC L ' is small, then even if the innovations of the skilled
only rarely employ unskilled, the unskilled will still come to the town because the cost of
living there is so modest. However, when ( )NC L ' is large then the skilled will push up
housing prices for the unskilled by such a large amount that they will not be willing to
pay to live around the skilled entrepreneurs. As such, a second possible reason why the
skilled increasingly locate around each other is that the housing supply has gotten more
inelastic over time, possibly as a result of land use regulations (Glaeser, Gyourko and
Saks, 2005).
We end this section by considering the impact of an increase in φ on wages, but in this
case we hold city populations fixed. A model of the form described above has essentially
perfect labor supply so that shocks to labor demand can only have a limited effect on
nominal wages and no effect on real wages. This could be modified by assuming
heterogeneous tastes for different locales, but this would complicate the situation
excessively. Instead, we simply assume that in some short run, city populations are fixed.
As such, this proposition should be seen as a partial equilibrium analysis that restricts
population movements to changes in φ . If population levels are allowed to move freely
with respect to changes in this parameter, then the differences in wages will be entirely
determined by differences in the cost of living functions and will not reflect different
demand for workers. To simplify matters further, we assume that 0== ii lh and find:
19
Proposition 2: The difference in wages between the skilled and unskilled will increase
with φ .
If higher skill levels in cities are caused by differential amenity levels or higher
levels of Hiθ then as φ rises, the sensitivity of average income to the share of high skilled
people in the area will also rise as long as f’’ is effectively constant in the range of
interest and 21
21
lhL
iH
i θθ > .
If αQQf =)( then the differences in the logarithm of wages between skilled and
unskilled that is associated with an increase in φ will be greater in areas where Li
Hi
NN
is
higher.
Proposition 2 provides the basis for our analysis in Section V where we look at the
changes in wages over time. The proposition has three parts. First, as φ rises this will
mean that there are more firms using skilled labor relative to firms using unskilled labor.
This causes labor demand for skilled workers to rise and this will increase the wages of
the skilled relative to the unskilled. This effect is not surprising, but it relates to the well
known rise in returns to skill over the last 25 years. If new firms make more use of
skilled workers, then this provides one possible reason for this phenomenon.
The second part of the proposition shows that the connection between area level skills
and area level income will increase as φ rises. The primary reason for this is that the
rise in returns to skill naturally means that the relationship between area level skills and
area level income will rise.
The third part of the proposition suggests that an increase in φ will cause greater wage
gaps between skilled and unskilled in more skilled areas. The reason for this is that
higher values of φ mean that the skilled entrepreneurs, who are more abundant in more
skilled cities, generally raise the wages of skilled laborers. A higher value of φ
20
essentially increases the degree of complementarity across skilled people since it means
that skilled people are more likely to end up hiring other skilled people.
IV. Skills, Innovation and Housing Supply
We now turn to evidence on changes in the ratio ( )NC L '1 φ−
. We start by documenting the
tendency of skilled innovators to hire skilled laborers. We then turn to the changes in
housing supply elasticity.
Skills and Innovation
One possible explanation for skill divergence among cities is that the innovations of
skilled entrepreneurs disproportionately utilize skilled workers. Although we are not
aware of a publicly available data source that would allow us to test this hypothesis
directly, we have assembled several pieces of evidence that are broadly consistent with
such an explanation.
Perhaps the most direct evidence on the relative level of human capital in new firms
comes from Abowd et al. (2001), who use a restricted access data set from the Census
Bureau’s Longitudinal Employer-Household Dynamics Program. Examining the Illinois
economy, the authors find that one important factor contributing to the overall increase in
human capital in the 1990s is that entering businesses had substantially more skilled
employees than exiting businesses. They note, however, that upskilling within
continuing businesses accounts for the largest share of the aggregate increase in skills.
This work does not specifically relate to the difference between skilled and unskilled
entrepreneurs, but if we believe that the majority of entrepreneurs are skilled, then this
fact supports our assumption that φ has changed.
Another testable implication of the model is that the pattern of skill divergence we
observe across cities also holds across industries. Using the census PUMS data, we
21
computed average educational attainment by 3-digit industry and examined whether
highly skilled industries have a tendency to become more skilled over time. Column one
of Table 5 shows this relationship. For each time period, there is a positive association
between the initial share of workers with a college degree and the growth in college
attainment over the succeeding decade. The association is only significant at the 10
percent level in the 1980s, however. The relationship between initial attainment and
subsequent upskilling is largest in the 1970s, suggesting that the rate of skill divergence
may have decreased over time. However, we are not able to reject the hypothesis that
skill divergence in the 1990s is equal to that observed in the 1970s.
We next investigate whether employment in more skilled industries is growing over time.
This fact might be understood as testing the hypothesis that skilled people are particularly
innovating in recent time periods. In every decade, we see a positive association
between initial college attainment in an industry and subsequent employment growth in
the industry. This result is simply a re-affirmation of the common finding in the wage
structure literature that between-industry demand shifts have favored college workers
(e.g., Katz and Murphy, 1992). The relationship is strongest in the 1980s, although we
cannot reject that the coefficients for the 1980s and 1970s are equal. We can, however,
reject that the relationship in 1990s is equal to either of the earlier decades, indicating that
the relationship between initial attainment and subsequent employment growth has
declined over time, consistent with Autor, Katz and Krueger (1998). In sum, two patterns
we observed across cities are also evident across industries; namely, the tendency for
highly skilled cities and industries to become more skilled over time and to add more
jobs.
While the above evidence on skill and employment growth across industries is consistent
with the basic hypothesis that skilled entrepreneurs disproportionately hire skilled
workers, we have still not shown an explicit link between the skills of entrepreneurs and
workers. Although we lack data on entrepreneurs specifically, we approach this problem
by computing educational attainment by occupation within industries. Using the census
22
PUMS, we compute the percentage of college graduates in three broad occupational
categories: managerial and proprietary, technical and professional, and all other workers.3
We compute these occupational attainment estimates by 3-digit industry code, excluding
farming and agriculture from the analysis. As shown in Table 6, we then correlate the
educational attainment among managers and owners with the educational levels for the
other groups. In 1970, across industries the correlation between manager’s education
levels and the education level of ordinary workers was 38 percent. In 2000, the
correlation between manager’s education level and the education level of ordinary
workers was 51 percent. This difference is strongly significant statistically.
Figure 3 shows the relationship between the share of managers with college degrees and
the share of ordinary workers with college degrees in 1970. The regression line in the
graph shows that on average a one percent increase in the share of managers with college
degrees is associated with a .15 percent increase in the share of ordinary workers with
college degrees. Figure 4 shows the same relationship for 2000. The regression line in
that growth shows that on average a one percent increase in the share of managers with
college degrees in 2000 is associated with a .38 percent increase in the share of ordinary
workers with college degrees. In other words, high skill managers increasingly manage
firms with high skill workers.
In Table 6, we also show the correlations between the education of managers and the
education of professional and technical workers. This correlation coefficient was .42 in
1970 and .64 in 2000. Again, the change is statistically significant. Highly skilled
managers and skilled technical workers have also increasingly concentrated within
industries.
3 Specifically, using the PUMS occupation codes (Ruggles et al. 2004), we classify individuals into three categories: Managers, Officials, and Proprietors (codes 200 to 290); Professional and Technical (codes 000 to 099); and all other workers. We exclude farming occupations (codes 100, 123, and 810 to 840) and those with missing values from the analysis.
23
Our findings are not definitive and there are substantial questions about causality in all of
our empirical findings, but our evidence suggests the idea that skilled entrepreneurs and
managers disproportionately hire skilled labor to be a promising explanation for skill
divergence across cities. The increasing correlation between managerial and worker
skill, and the persistent tendency for initial skilled industries to become more skilled over
time provides some evidence for this view. These results are also broadly consistent with
Kremer and Maskin’s (1996) finding of increasing segregation of high- and low-skill
workers into separate firms.
Housing Supply
A second possible explanation for the increasing tendency of skilled cities to become
more skilled is that housing supply appears to have become more inelastic. While we
lack compelling measures of supply elasticity, there are a variety of pieces of evidence
that do point toward an increasing inability to build more housing cheaply. In this
section, we summarize that evidence.
The first piece of evidence pointing toward this inelasticity is the increasing gap between
housing prices and construction costs. In 1970, in almost every metropolitan area, most
houses were valued at less than 1.25 times construction costs. Ninety percent of the areas
in a 102 metropolitan area sample had an average price that was less than twelve percent
more than construction cost. Thirty years later in the average metropolitan area, housing
prices cost more than 46 percent more than construction costs (Glaeser, Gyourko and
Saks, 2005). These prices must reflect increasing difficulties of building readily.
A second piece of evidence suggesting declining housing supply elasticity is the
declining number of new homes that are being built, particularly in high cost areas. In a
sample of homes in 102 metropolitan areas, the median metropolitan area in 1970 built
35 percent of its homes over the previous decade. In 2000, the median metropolitan area
built only 14 percent of its homes over the previous decade (Glaeser, Gyourko and Saks,
24
2005). Detailed analysis of particular metropolitan areas shows a stunning decline in
permitting between 1960 and today (Glaeser, Gyourko and Saks, 2004).
A third piece of evidence showing declining elasticity is that the connection between
housing prices and new construction is falling. Glaeser, Gyourko and Saks (2004) show
that in the 1960s and 1970s in New York City, new construction increases when housing
prices rise. In the 1990s, this correlation disappears. Glaeser, Gyourko and Saks (2005)
find across metropolitan areas that higher housing prices are becoming more negatively
associated with new construction over time. This decline is consistent with an increasing
inability to build in high cost regions.
But while there is evidence suggesting that housing supply has become more inelastic
over time, there is little evidence suggesting that the housing price premium associated
with living in a better educated city has increased. If we regress median housing values
in 1980 on the share of adults with bachelor’s degrees during that year, we estimate:
(8) ( ) 1980)241(.)042(.1980 012.322.10 CollegeValueLog •+=
Standard errors are in parentheses and there are 318 observations. The r-squared is 33
percent. Data are from the census and housing values are in 2000 dollars.
The same regression in 2000 yields:
(9) ( ) 2000)207(.)051(.2000 007.388.10 CollegeValueLog •+=
There are 318 observations and the r-squared is 40 percent. Data are from the census.
There has been a tendency of housing prices to rise in highly educated areas, but
generally the price increase has been lower than the price increase that would be
suggested by rising wages in those areas (Glaeser and Saiz, 2004).
25
A second piece of evidence suggesting that high housing prices are not driving the
increasing tendency of the skilled to move toward skilled areas is that controlling for
lagged housing prices does little to change to relationship between initial skill levels and
the growth in the share of the population with at least sixteen years of schooling. For
example if we modify our basic regression from Table 1 to include the lagged median
housing value, we estimate:
(10) )(001.139.004. 1990)002(.1990)014(.)02(.19902000 ValueLogCollegeCollegeCollege •+•+−=−
where )( 1990ValueLog refers to the logarithm of median housing value in the metropolitan
area in 1990. The r-squared in this regression is 28 percent and there are 318
observations. The coefficient on share with sixteen years of schooling or more is
essentially unchanged from that reported in Table 1, regression 1. The coefficient on the
lagged median housing value is essentially zero. There is no sense that controlling for
lagged housing prices impacts the relationship between initial share of the adult
population with sixteen years of schooling or more and later growth in that variable.
Overall, there is little evidence supporting the idea that increasing inelastic housing can
explain the divergence of human capital levels. While housing supply is becoming more
inelastic, there has been a substantially higher cost associated with living in educated
metropolitan areas for many decades. As a result, it doesn’t seem likely that high
housing prices are the main reason for the increasing tendency of the skilled to live in
more skilled areas.
V. Evidence on Income Patterns across Metropolitan Areas
Finally, we turn to the implications of skill agglomerations for wages and income
patterns. First we turn to the correlations between area level skills and area level income.
Second, we turn to patterns of metropolitan area income convergence.
26
Income and Education across Metropolitan Areas
The model suggested that if the tendency of skilled entrepreneurs to employ skilled
laborers is rising, we should expect an increasing correlation between area level skills and
area level income. Indeed, the correlation between education and income is also
increasing. Figure 5 shows the relationship between the percent of the population with a
college degree and the logarithm of per capita income at the metropolitan area level in
2000. The income data come from REIS and educational attainment from the census.
The regression line shown in the figure is:
(11) ( ) 2000)11(.)02(.2000 63.18.9 CollegeIncomeLog •+=
The r-squared of this regression is 40 percent and there are 318 observations. In 1970,
the relationship is much weaker as shown in Figure 6. The regression line in this case is:
(12) ( ) 1970)21(.)02(.1970 84.01.8 CollegeIncomeLog •+=
There are again 318 observations and the r-squared is 4.6 percent. The correlation
between the logarithm of mean income in the metropolitan area and the percent of the
population with college degrees increases from 21.4 percent in 1970 to 32.2 percent in
1980 to 49.8 percent in 1990 to 63.3 percent in 2000.
While these trends are impressive, these results in no sense correct for the general rise in
returns to skill. To do this, we follow Rauch (1993) and turn to individual level
regressions where we examine the changing correlation between metropolitan area level
skills and wages holding individual skills constant. Our basic specification is:
(13) ControlsOtherSchoolingSchoolingWageLog tMSAttittMSAi +•+•= ,,,, )( βα
27
Data are from the PUMS (Ruggles et al. 2004).4 For each individual, the logarithm of
hourly income for individual i at time t living in a particular metropolitan area
( )( ,, tMSAiWageLog ) is regressed on their own education and the percentage of adults with
a college degree in the metropolitan area ( tMSASchooling , ). The coefficients on both
individual schooling and metropolitan area level schooling are allowed to change over
time. We estimate the individual schooling effects by including dummy variables for
individual years of education. We include only males between 25 and 55 with complete
observations. We control for race using dummy variables and for age by using a fourth
order polynomial. The coefficients are also allowed to change over time.
In all of our regressions, we use average schooling in 1970 as our measure of
metropolitan area schooling and estimate its effect on individual wages in 1980, 1990,
and 2000. This has the effect of limiting the endogeneity of our key independent variable
and of focusing on the wage effects of initially high skilled cities. If we used
contemporaneous schooling levels, then the correlation with wages is almost sure to be
the result of omitted variables that both raise demand for high skilled workers in the
region and later attract more skilled people into that region.
The results are shown in Table 7. The first equation shows our basic results, which echo
those of Rauch (1993) and Glaeser and Saiz (2004). There is a strong basic connection
between the share of college graduates in the metropolitan area and the logarithm of the
hourly wage. Each extra percent of adults with a college degree is associated with .58 log
points of extra income in 1980. This effect rises over time and in 2000, each extra
percent of metropolitan area college attainment is associated with 1.22 log points of extra
income. The f-tests reported in the bottom row of the table confirm that this change is
statistically significant.
Perhaps the most significant issue with this Rauch (1993) type regression is the
possibility that metropolitan area schooling is correlated with unobserved individual
4 For each PUMS year, we use the sample with the richest metropolitan area coverage, which is the 1 percent sample in 1970, 1980, and 1990, and the 5 percent sample in 2000 (Ruggles at al. 2004).
28
human capital. After all, since more skilled metropolitan areas are defined on the basis of
people with more observed human capital sorting into them, it would not be surprising
that people with more unobserved human capital also sort into them. If we are willing to
accept that this sorting has not changed over time and that the coefficient on unobserved
ability is not changing over time (both of which are quite debatable assumptions), then
controlling for metropolitan area fixed effects is one way of addressing the problems
related to unobserved ability sorting.
In regression (2) of Table 7, we repeat our basic specification including metropolitan area
fixed effects. As such, we can no longer estimate a baseline relationship between
metropolitan area years of schooling and the logarithm of hourly wages. However, we
can estimate the extent to which metropolitan area schooling has become a more
important predictor over time by looking at the interaction between metropolitan area
schooling in 1970 and dummy variables for the years 1990 and 2000. Again, the
regression shows a significant increase in the correlation between MSA level education
and individual wages. The coefficient on education rises by .51 between 1980 and 1990
and .16 between 1990 and 2000. Including MSA fixed effects does little to change the
basic relationships identified in regression (1).
In regressions (3)-(5), we reproduce regression (1) of Table 7 for different education
subgroups (results including MSA fixed effects are quite similar). In this case, we are
looking at whether there has been a change in the correlation between metropolitan area
education and wages for different subgroups and this represents a test of the prediction of
proposition 2 that an increase in the parameter φ , which represents the tendency of high
human capital entrepreneurs to hire their own, will lead to higher wages particularly for
high skilled workers. We divide the population into people with 16 years of education or
more, between 12 and 16 years of education and strictly less than 12 years of education.
This follows the work of Mare (1995) who identified different Rauch (1993) effects
among education subgroups.
29
In regression (3), we see the changing impact of area-level education on high school
dropouts. The effect only gets slightly stronger over time. The coefficient rises from .75
to 1.15, and we cannot reject that the coefficients for 1980 and 2000 are equal. In
regression (4), we report results for high school graduates and those with some college.
In this case, the basic effect is stronger and the coefficient rises between 1980 and 2000
from .45 to 1.08. For this group, all of the increase appears to have come between 1980
and 1990, as we cannot reject that the coefficients for 1990 and 2000 are equal. In
regression (5), we report results for college graduates and in this case the coefficient rises
from .68 to 1.41. The correlation between area level education and individual wages is
about even for college graduates and for high school dropouts in 1970, but by 2000 a gap
emerges in which the highly skilled benefit most from being around other skilled
workers.
These regressions treat metropolitan area level schooling as exogenous, which may not
be appropriate. After all, the major theme of the paper is the sorting of skilled people
into more skilled areas. Thus, we prefer to see these empirical results as tests of one
implication of the model rather than as estimates of a meaningful economic parameter.
The End of Regional Convergence?
In this final empirical section, we present what may be one of the most interesting
consequences of increased sorting by skill: the decline of metropolitan area convergence.
The basic convergence regression is:
(14) ( ) ControlsOther IncomeMSA IncomeMSA IncomeMSA
1-t1-t
t +•+=���
����
�LogLog βα
This regression is known to be biased downwards if there is time varying measurement
error in metropolitan area income. A significant literature (e.g. Barro and Sala-i-Martin,
1992) has documented a general pattern of regional convergence, and also reports a
decline in the amount of convergence in the 1980s relative to earlier time periods.
30
In Table 8, we estimate these convergence patterns for the 1970s, 1980s and 1990s using
two different measures of income: average wage and per capita income, both from REIS.
In the Table 8a, we include only initial income as a regressor. Both measures of income
data show the same pattern. There was substantial convergence in the 1970s which
decreased over time. In the case of the wage data, shown in regressions (1)-(3), the
coefficient on initial income is -.06 in the 1970s and .02 in the 1990s. These coefficients
move from being significantly negative to being significantly positive. Figure 7 shows
wage convergence in the 1970s; Figure 8 shows wage divergence in the 1990s.
Regression (4)-(6) of Table 8a show the results for income. In this case, convergence in
the 1970s is even more striking and the basic coefficient is -.11. In the 1990s, the
coefficient estimate is positive but not statistically significant. The change in coefficients
for income is even larger than the change in coefficients for wages. In the 1970s, poorer
metropolitan areas were getting richer relative to richer metropolitan areas. In the 1990s,
richer areas got richer relative to poorer areas.5
One potential explanation for this fact is the rise in returns to skill and the increased
sorting across metropolitan areas. In the Table 8b, we repeat our convergence
regressions controlling for the change in the share of the adult population with college
degrees in the metropolitan area. This control eliminates all signs of divergence. When
we use log of wages in the first three regressions there is still a substantial decline in the
level of convergence over the past 30 years. When we use log of income in the last three
regressions, the change in the amount of convergence is more modest and it does appear
that controlling for the change in the share of the population with college degrees
explains the decline in regional convergence.
Convergence has declined substantially over the last 30 years. One potential reason for
this is that initial high income, and high skill, places are increasingly attracting more
5 Barro and Sali-i-Martin (1999) find that convergence in personal income across U.S. states appeared to end in the 1980s, a result which they attribute to oil shocks. They do not report results for the 1990s.
31
skilled people. When we control for the changes in the skill composition at the area
level, convergence reappears although there still seems to be some change between the
1970s and the 1990s.
VI. Conclusion
In this paper, we have documented that places with higher levels of human capital have
attracted more skilled people over the last three decades. The correlation between the
initial share of metropolitan area adults with college degrees and change in that variable
over the 1990s is enormously strong. Educated people are still remarkably spread out
across areas, but it is possible that segregation by skill might become more significant
over time if this trend continues.
One potential explanation for this phenomenon is that labor demand is often created by
local entrepreneurs who start firms in their own city. If skilled people are increasingly
likely to start firms that hire other skilled people, then this could readily explain why an
initially high level of skills would lead to a growth in the skill composition of a city over
time. The initial population starts new firms and hires new skilled people. According to
this view, the key change over the last 30 years is that high skill entrepreneurs
increasingly innovate in ways that lead to more employment for other skilled people.
There is some evidence that such a change has occurred. The correlation between the
skill level managers and workers within industries has been rising over time. The wages
for skilled workers in skilled cities have been rising relative to the wages of unskilled
workers in the same cities. This is a prediction of a model where the skill level in a place
leads to an increase in labor demand particularly for skilled workers.
While it seems that the tendency of the skilled to move to skilled areas is partly
responsible for the remarkable decline in income convergence across metropolitan areas,
it is not obvious that a public policy response to this change is needed or appropriate.
After all, basic results in welfare economics tell us that while wealth differences across
32
people may be important, wealth differences across places are not necessarily troubling.
Unless we are confident that the increasing tendency of skilled cities to become more
skilled creates negative externalities for the unskilled, these results suggest interesting
changes across America’s cities but they do not suggest any definite policy action.
33
References
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Autor, D., Katz, L. and A. Krueger (1998) “Computing Inequality: Have Computers Changed the Labor Market?” Quarterly Journal of Economics 113(4): 1169-1213.
Barro, R. and X. Sala-i-Martin (1992) “Convergence” Journal of Political Economy 100(2): 223-251.
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and the Life Cycle of Products” American Economic Review 91(5): 1454-1477. Glaeser, E, Gyourko, J. and R. Saks (2005) “Why Have Housing Prices Gone Up?”
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34
Table 1 -
1990-2000 1980-1990 1970-1980
Change in percentage of adults with bachelor’s
degree
Change in percentage of adults with bachelor’s
degree
Change in percentage of adults with bachelor’s
degree
(1) (2) (3) (4) (5) (6)
Share with bachelor's degree (age 25+) at t-10 0.1376090 0.1173534 0.1296989 0.1472086 0.2433141 0.2050632 (0.0124199) (0.0144661) (0.0147455) (0.0136836) (0.0180609) (0.0199073) Log of population at t-10 0.0004802 0.0053672 0.0030759 (0.0008472) (0.0007268) (0.0008470) Share of workers in manufacturing at t-10 0.0278880 0.0183154 -0.0222402 0.0116913 (0.0086370) (0.0086630) Log of per capita income at t-10 0.02515 0.0046874 0.0117082 (0.0059294) (0.0050577) (0.0060210) Regional fixed effects No Yes No Yes No Yes Observations 318 318 318 318 318 318 R squared 0.2798 0.4001 0.1967 0.516 0.3648 0.4477
Standard errors in parentheses. Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in
New England). All data are from the 1970, 1980, 1990 and 2000 US censuses. County level data from each census are aggregated to a consistent set of metropolitan area boundaries as defined by the Office of Management and Budget in 1999.
35
Table 2 -
1990-2000 1980-1990 1970-1980
Log change in number of adults with
college degree
Log change in number of adults w.o.
college degree
Log change in number of adults with
college degree
Log change in number of adults w.o.
college degree
Log change in number of adults with
college degree
Log change in number of adults w.o.
college degree
(1) (2) (3) (4) (5) (6)
Share with bachelor's degree (age 25+) at t-10 0.1920509 0.0671524 0.3119436 0.3057507 0.0552201 0.5958813 (0.1019708) (0.0824342) (0.1387881) (0.1258663) (0.2062770) (0.1961645) Observations 318 318 318 318 318 318 R squared 0.0111 0.0021 0.0157 0.0183 0.0002 0.0284 Constant 0.2768968 0.0794055 0.3337489 0.1051539 0.6430823 0.1269587 Test: coefficient for adults with college degree equals coefficient for adults w.o. college degree
Chi squared statistic p-value
2.95 0.086
0.00 0.945
18.93 0.0000
Standard errors in parentheses. Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in
New England). All data are from the 1970, 1980, 1990 and 2000 US censuses. County level data from each census are aggregated to a consistent set of metropolitan area boundaries as defined by the Office of Management and Budget in 1999.
36
Table 3: 1970s 1980s 1990s Dependent Variable: Change in Industrial Skill Index
Initial share of BAs .0346519 (.0086341)
-.0038652 (.007843)
.0031569 (.008467)
Observations 318 318 318 R squared 0.0485 0.0008 0.0004 Constant .0701384 .0313898 .0315159
Dependent Variable: Change in MSA Education minus Industrial Skill Index
Initial share of BAs .2086622 (.0184751)
.1335641 (.0159062)
.1344521 (.0142837)
Observations 318 318 318 R squared 0.2876 0.1824 0.2190 Constant -.0451122 -.0190977 -.0215653
Standard errors in parentheses.
Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England). Share of BAs is obtained from the US census. County level data from each census are aggregated to a consistent set of metropolitan area boundaries as defined by the Office of Management and Budget in 1999. The Industrial Skill Index is based on data from the Regional Economic Information System (REIS) of the Bureau of Economic Analysis and the public use micro-samples (PUMS) of the U.S. Census, as defined in the text.
37
Table 4: Segregation by Skill
Year Mean share
BAs across
Metropolitan
Areas
Standard
Deviation
25-75
Difference
Dissimilarity
Index
Isolation
Index
1970
.112 .042 .045 .110 .008
1980
.164 .054 .063 .114 .011
1990
.187 .063
.077 .123 .013
2000
.226 .073 .096 .128 .016
Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England). All data are from the 1970, 1980, 1990 and 2000 US censuses. County level data from each census are aggregated to a consistent set of metropolitan area boundaries as defined by the Office of Management and Budget in 1999. Formulas for the dissimilarity and isolation indices are given in the text.
38
Table 5
1970s 1980s 1990s Dependent Variable: Change in Percent BAs in Industry
Initial Share of BAs in Industry .1111996 (.0255809)
.0370845 (.0209052)
.063308 (.0245295)
Observations 142 142 133 R squared 0.1189 0.0220 0.0484 Constant .0467842 .0238306 .0132863
Dependent Variable: Log Change in Industry Employment
Initial Share of BAs in Industry 1.13637 (.2095189)
1.481435 (.2222994)
.4701833 (.2243097)
Observations 142 142 133 R squared 0.1452 0.2445 0.0255 Constant .0485614 -.0937727 -.0812391
Standard errors in parentheses. Data are from the 1970, 1980, 1990, and 2000 PUMS. Educational attainment and total employment are computed for a consistent set of three-digit industry codes, using the PUMS variable ind1950 (Ruggles et al. 2004). Each observation is one three-digit industry.
39
Table 6: Changing Correlation between Education of Managers and Workers Worker BA
Attainment Tech./Prof. BA Attainment
Manager/Proprietor BA Attainment
1970 Worker BA Attainment
1.0000
Tech./Prof. BA Attainment
0.3508 1.0000
Manager/Proprietor BA Attainment
0.3846 0.4246 1.0000
2000 Worker BA Attainment
1.0000
Tech./Prof. BA Attainment
0.5035 1.0000
Manager/Proprietor BA Attainment
0.5147 0.6367 1.0000
Data are from the 1970 and 2000 PUMS (Ruggles et al. 2004). Workers are classified into one of the three occupational categories as described in the text, using the PUMS variable occ1950. Educational attainment is computed by occupational category within three-digit industry codes, using the PUMS variable ind1950. Each observation is a three-digit industry x occupational category.
40
Table 7: IPUMS Estimates of Effects of MSA-Level Education on Individual Wages
Total Sample Total Sample Did Not Graduate High School
High School Graduates, No BA
College Graduates
(1) (2) (3) (4) (5) 1970 Pct BAs x 1980 dummy
.5771157 (.2619824)
Omitted .7529274 (.372206)
.453735 (.2762018)
.6831703 (.2781051)
1970 Pct BAs x 1990 dummy
1.130842 (.2550705)
.5123142 (.0548032)
1.308788 (.3094018)
1.180671 (.2745616)
.9964586 (.2645873)
1970 Pct BAs x 2000 dummy
1.219518 (.2147136)
.6692932 (.0428129)
1.151335 (.2275083)
1.080403 (.2104377)
1.414034 (.2699609)
MSA fixed effects No Yes No No No R-squared .1919 .2092 .0816 .0991 .0967 Observations 2938321 2938321 347696 1681883 908742 F test: 2000=1980 0.0033 0.0000 0.2190 0.0068 0.0081 F test: 2000=1990 0.4743 0.0001 0.4505 0.4805 0.0065 F test: 1990=1980 0.0102 0.0000 0.1091 0.0027 0.1199
Note: Robust standard errors clustered by MSA in parentheses. Data are from the 1970, 1980, 1990, and 2000 PUMS. Regressions include year fixed effects and controls for age up to a 4th degree polynomial, race, Hispanic status, and individual education. All controls are allowed to vary by year. Total sample includes all males aged 25 to 55 who worked at least 10 hours per week. Individuals with missing or imputed values for any of the variables are excluded. The dependent variable is the logarithm of the individual’s hourly wage.
41
Table 8a: Trends in Regional Convergence Log Change in
Wages, 1970-80 Log Change in
Wages, 1980-90 Log Change in Wages, 1990-
2000
Log Change in Income, 1970-
80
Log Change in Income, 1980-
90
Log Change in Income, 1990-
2000 (1) (2) (3) (4) (5) (6)
-0.060 0.025 0.019 -0.114 -0.062 0.014 Initial Log Wages/Income (0.009) (0.010) (0.007) (0.022) (0.030) (0.020) Constant 1.798 0.303 0.254 1.876 1.195 0.265 (0.116) (0.140) (0.102) (0.182) (0.276) (0.198) Observations 318 318 318 318 318 318 R-squared 0.13 0.02 0.02 0.08 0.01 0.00 Standard errors in parentheses Table 8b Log Change in
Wages, 1970-80
Log Change in Wages, 1980-
90
Log Change in Wages, 1990-
2000
Log Change in Income, 1970-
80
Log Change in Income, 1980-
90
Log Change in Income, 1990-
2000 (1) (2) (3) (4) (5) (6)
-0.074 -0.023 -0.001 -0.150 -0.201 -0.090 Initial Log Wage/Income (0.008) (0.010) (0.006) (0.023) (0.022) (4.51)
3.841 6.939 4.230 0.985 4.188 2.250 Change in Share of Adults with College Degree
(0.591) (0.707) (0.463) (0.225) (0.226) (10.51)
Constant 1.780 0.754 0.392 2.117 2.327 1.202 (0.109) (0.131) (0.092) (0.186) (0.201) (6.24) Observations 318 318 318 318 318 318 R-squared 0.23 0.25 0.23 0.13 0.53 0.26 Standard errors in parentheses Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England), using constant 1999 boundaries. Income and wage data are from REIS. Educational attainment is from the census.
42
Figure 1
0.0
5.1
Cha
nge
in P
erce
nt w
ith B
A 1
990-
2000
.1 .2 .3 .4 .5Percent of Adults with BA Degree in 1990
Figure 2
0.0
2.0
4.0
6.0
8.1
Cha
nge
in P
erce
nt w
ith B
A 1
980-
1990
.1 .2 .3 .4Percent of Adults with BA Degree in 1980
Note for Figures 1 and 2: Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England), using constant 1999 boundaries. Data are from the census.
43
Figure 3
0.1
.2.3
.4S
hare
of N
on-T
echn
ical
Wor
kers
w B
A in
197
0
0 .2 .4 .6 .8Share of Managers w BA in 1970
Figure 4
0.2
.4.6
Sha
re o
f Non
-Tec
hnic
al W
orke
rs w
BA
in 2
000
0 .2 .4 .6 .8Share of Managers w BA in 2000
Note for Figures 3 and 4: Data are from the PUMS. Each circle represents one 3-digit industry. Managers and non-technical workers are defined as described in the text.
44
Figure 5
9.5
1010
.511
Log
of P
er C
apita
Per
sona
l Inc
ome
in 2
000
.1 .2 .3 .4 .5Share of Adults with BA Degree in 2000
Figure 6
7.5
88.
59
Log
of P
er C
apita
Per
sona
l Inc
ome
in 1
970
.05 .1 .15 .2 .25 .3Share of Adults with BA Degree in 1970
Note for Figures 5 and 6: Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England), using constant 1999 boundaries. Income data are from REIS and educational attainment from the census.
45
Figure 7
.6.8
11.
21.
41.
6Lo
g C
hang
e in
Avg
Wag
e 19
70-8
0
10 12 14 16 18Average Wage in 1970
Figure 8
.2.4
.6.8
11.
2Lo
g C
hang
e in
Avg
Wag
e 19
90-2
000
12 14 16 18 20Average Wage in 1990
Note for Figures 7 and 8: Observations include all 318 metropolitan statistical areas and primary metropolitan statistical areas (NECMA definitions in New England), using constant 1999 boundaries. Data are from REIS.
46
Appendix: Proofs of Propositions
Proof of Proposition 1: Differentiating equations ( )( ) UANNCWU Hi
Li
Hi
HHi =+− , and
( )( ) UANNCWU Li
Li
Hi
LLi =+− ,, gives us that 1=
∂∂
=∂∂
H
Hi
L
Li
CW
CW
, 01
2 <−=∂∂
UU
AW
Li
Li ,
01
2 <−=∂∂
UU
AW
Hi
Hi .
For any exogenous parameter “x” that enters directly into the equation
( )( )Li
Hi
LLi
LiL
iHii
LiL
i NNCAWNlNhl
Nf +=��
�
����
�
+−+′ ,
)1( 11φθ but not into the equation
( )( )Li
Hi
HHi
HiH
ii
HiH
i NNCAWNhh
Nf +=��
�
����
�
+′ ,
1φθ it follows that:
( )( )
( ) ( ) xN
NCNhh
hQfNC
xN L
i
H
Hii
iHH
i
HHi
∂∂
′++
′′−
′−=∂
∂
2
1φθ
, and since( )
( )( ) ( )
10
2
1
−>′+
+
′′−
′−>NC
Nhh
hQfNC
H
Hii
iHH
i
H
φθ
then x
Nx
N Hi
Li
∂∂
>∂
∂ with opposite sign.
For Lix θ= , differentiation yields
( )( )
( )( ) ��
�
����
�
∂∂
+∂∂′+
+−+
∂∂
−−∂∂
−+′′−=��
�
����
�
+−+′
Li
Li
Li
HiL
Li
Hii
Li
HiL
iLi
LiH
ii
LL
iLi
Hii
Li
NNNC
NlNhl
NNh
NNhl
QfNlNhl
Nf
θθ
φθ
φθ
φθ
φ 2
11
11
11 )1(
)1()1(
)1(
Assume Li
Li
Li
Hi NN
θθ ∂∂
≥≥∂∂
0 , and in that case both terms on the right side of the equation
are non-positive and there is a contradiction so L
i
Hi
Li
Li NN
θθ ∂∂
>>∂∂
0 .
47
For ilx = ,
( ) ( ) ( )
( )( )
( )2
11
11
2
11
)1(
)1()1(
')1(
Li
Hii
i
HiL
ii
LiH
ii
LL
i
i
Li
i
HiL
Li
Hii
Li
LL
i
NlNhl
lN
Nhl
NNhl
Qf
lN
lN
NCNlNhl
NQf
+−+
∂∂
−−∂
∂−+
′′−
���
����
�
∂∂
+∂
∂=
+−+′′−
φ
φφθ
φθ
. If we
assume that i
Li
i
Hi
lN
lN
∂∂
≥≥∂
∂0 , the right hand side of the equation is non-positive and
there is a contradiction so this proves that i
Hi
i
Li
lN
lN
∂∂
>>∂
∂0 .
For LiAx = ,
( )( )
( )( ) ��
�
����
�
∂∂
+∂∂
+
+−+
∂∂
−−∂∂
−+′′−=
∂∂
−
Li
Li
Li
HiL
Li
Hii
Li
HiL
iLi
LiH
ii
LL
iLi
Li
AN
AN
NC
NlNhl
AN
NhAN
NhlQf
AW
'
)1(
)1()1(
2
11
11
φ
φφθ
and again
if we assume that Li
Li
Li
Hi
AN
AN
∂∂
≥≥∂∂
0 , the right hand side of the equation is non-positive
and there is a contradiction so Li
Hi
Li
Li
AN
AN
∂∂
>>∂∂
0 .
For any exogenous parameter “x”, that enters directly into the equation
( )( )Li
Hi
HHi
HiH
ii
HiH
i NNCAWNhh
Nf +=��
�
����
�
+′ ,
1φθ but not into the equation
( )( )Li
Hi
LLi
LiL
iHii
LiL
i NNCAWNlNhl
Nf +=��
�
����
�
+−+′ ,
)1( 11φθ , it follows that:
48
( ) ( ) ( )
( ) ( ) ( ) xN
NCNlNhl
NhlQf
NCNlNhl
NhQf
xN H
i
L
Li
Hii
Hii
LL
i
L
Li
Hii
Li
LL
iLi
∂∂
++−+
−+′′−
−+−+
−′′−
=∂
∂
')1(
)1(
')1(
)1(
2
11
1
2
11
1
φφθ
φφθ
. The denominator of this
expression is always positive. The numerator is positive if and only if
( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+>−
θφφ
, which since ( )
( ) LiL
Li
Li
Hii
NhQfNlNhl
1
2
11)1(′′−
+−+θ
φ is a
positive finite number will always hold if ( )NC L '1 φ−
is sufficiently high and will never hold
if ( )NC L '1 φ−
is sufficiently low. If ( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+>−
θφφ
, then the signs of
xN L
i
∂∂
and x
N Hi
∂∂
must be the same and if ( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+<−
θφφ
then the
signs of x
N Li
∂∂
and x
N Hi
∂∂
must be opposite.
When ( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+<−
θφφ
, then x
Nx
N Li
Hi
∂∂
>∂
∂ because
( ) ( ) ( )
( ) ( ) ( )1
')1(
)1(
')1(
)1(
0
2
11
1
2
11
1
−>+
+−+
−+′′−
−+−+
−′′−
>NC
NlNhl
NhlQf
NCNlNhl
NhQf
L
Li
Hii
Hii
LL
i
L
Li
Hii
Li
LL
i
φφθ
φφθ
.
When Hix θ= , then differentiation of the first equality yields,
( ) ( ) ( ) ( ) ( )NCN
NCNhh
hQf
NQf H
Hi
LiH
Hii
iH
HiH
i
Hi
H ''2
1θφ
θθ ∂
∂+��
�
�
��
�
�+
+′′−
∂∂
=′
49
and if ( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+>−
θφφ
, so x
N Li
∂∂
and x
N Hi
∂∂
have the same sign, then
0>∂∂
Hi
HiN
θ and 0>
∂∂
Hi
LiN
θ. When ( )
( )( ) L
iLL
i
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+<−
θφφ
, then
xN
xN L
iHi
∂∂
>∂
∂, so it would be impossible for
Hi
Hi
Hi
Li NN
θθ ∂∂
≥≥∂∂
0 since that would imply
that ( ) ���
����
�
∂∂
+∂∂′>
Hi
Li
Hi
Hi NN
NCθθ
0 and therefore H
i
Li
Hi
Hi NN
θθ ∂∂
>>∂∂
0 .
When ihx = , differentiation yields
( ) ( ) ( ) ( ) ( ) ( )NCh
NNC
Nhh
hQf
hN
Nhh
NQf H
i
LiH
Hii
iH
Hi
i
Hi
Hii
Hi
HH
i ''2
1
2
1∂
∂+��
�
�
��
�
�+
+′′−
∂∂
=+
′′−φ
θφ
θ
and if ( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+>−
θφφ
, then 0>∂
∂
i
Hi
lN
and 0>∂
∂
i
Li
lN
. When
( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+<−
θφφ
, then x
Nx
N Li
Hi
∂∂
>∂
∂, so it would be impossible for
i
Hi
i
Li
hN
hN
∂∂
≥≥∂
∂0 and therefore
i
Li
i
Hi
hN
hN
∂∂
>>∂
∂0 .
When HiAx = , differentiation yields:
( ) ( ) ( ) ( )NCAN
NCNhh
hQf
AN
AW H
Hi
LiH
Hii
iH
HiH
i
Hi
Hi
Hi ''2
1∂∂
+��
�
�
��
�
�+
+′′−
∂∂
=∂∂
−φ
θ and if
( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+>−
θφφ
, then 0>∂∂
Hi
Hi
AN
and 0>∂∂
Hi
Li
AN
. When
50
( )( )
( ) LiL
Li
Li
Hii
L NhQfNlNhl
NC 1
2
11)1('
1′′−
+−+<−
θφφ
, then x
Nx
N Li
Hi
∂∂
>∂
∂, so it would be impossible for
Hi
Hi
Hi
Li
AN
AN
∂∂
≥≥∂∂
0 and therefore Hi
Li
Hi
Hi
AN
AN
∂∂
>>∂∂
0 .
Proof of Proposition 2: The wages of the skilled equal ���
����
�′1
1h
fHi φ
θ and the derivative
of this with respect to φ equals ���
����
�′′−11
2
1h
fh
Hi
φφθ
which is positive. The wages of the
unskilled equals
�����
�
�
�����
�
�
+−′
11)1(
1
lNN
hf
Li
Hi
Li
φθ and the derivative of this with respect to φ
equals
�����
�
�
�����
�
�
+−′′
���
����
�+− 11
2
11
1
)1(
1
)1( lNN
hf
lNN
h
NN
h
Li
Hi
Li
Hi
Li
HiL
i
φφ
θ which is negative.
If z denotes the share of high skilled people in the area, then average income is
����
�
�
����
�
�
+−
−′−+��
�
����
�′=11
1
1)1(
1)1(
1
lz
zh
fzh
fzY Li
Hi
φθ
φθ . Allowing H
iθ and HiA to vary and
differentiating totally yields:
Hi
Li
Li
Hi
dh
fzdz
lz
zhf
lz
zh
zh
lz
zhf
hf
Yd θφ
φφ
φθ
φθφ
θ
���
����
�′+
����������
�
�
����������
�
�
����
�
�
����
�
�
+−
−′′
��
���
� +−
−
−−
−����
�
�
����
�
�
+−
−′−��
�
����
�′
=1
11
2
11
1
111
1
1)1(1
1)1(
)1(1
1)1(11
51
where HiH
i
HiH
i
dAAz
dz
dz∂∂+
∂∂= θθ
. The coefficient on dz represents the sensitivity of
Y to changes in z, while the coefficient on Hidθ represents the additional sensitivity of
income for changes in z due to an increase in Hiθ rather than H
iA . Both coefficients will
be positive provide that Li
Hi θθ > and the number of firms employing low skill workers
exceeds the number of firms employing high skill workers. Differentiating the coefficient
on dz with respect φ but holding population constant
yields
�����
�
�
�����
�
�
��
���
� +−
−
���
����
�−
−+−
+ 3
11
1211
12
1)1(
)1()1(
)1(
lz
zh
lz
zzhh
h
LiH
i
φ
φθ
φθα where terms involving f’’’(.) have been
dropped and f’’(.) has been assumed to be constant at α− . Our goal is to show that this
expression is positive when 21
21
lhL
iH
i θθ > by showing that 3
11
11
12
1)1( �
�
���
� +−
−
−>
lz
zh
lhh
Li
Hi
φ
θφθ
.
The left-hand side of this inequality is decreasing in φ and the right-hand side is
increasing in φ so the inequality is strictest when 1=φ , giving 21
21
lhL
iH
i θθ > . Thus when
21
21
lhL
iHi
θθ > the coefficient on dz in the total differential of Yd is increasing inφ . To see
that the coefficient on Hidθ is also increasing inφ , differentiate to obtain
���
����
�−
112
1''
hf
hz
φφwhich is positive.
If αQQf =)( , then the difference of the logarithm of wages between skilled and
unskilled people equals ( ) ( ) ��
�
�
��
�
����
����
�+−−−+��
�
����
�111 )1(1 l
NN
hLoghLogLogLi
Hi
Li
Hi φφα
θθ
and the